Maths-
General
Easy

Question

If f(x) is twice differentiable function f((1)=1, f(2)=4, f(3)=9

  1. f to the power of ’ end exponent left parenthesis x right parenthesis equals 2, for atleast one in x element of left parenthesis 13 right parenthesis    
  2. f to the power of ’ end exponent left parenthesis x right parenthesis equals f left parenthesis x right parenthesis equals 5, for some x element of left parenthesis 23 right parenthesis    
  3. f to the power of ’ end exponent left parenthesis x right parenthesis equals 3 comma for all element of left parenthesis 23 right parenthesis    
  4. f to the power of ’ end exponent left parenthesis x right parenthesis equals 2, for some x element of left parenthesis 12 right parenthesis    

The correct answer is: f to the power of ’ end exponent left parenthesis x right parenthesis equals 2, for atleast one in x element of left parenthesis 13 right parenthesis

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If f(x) equals x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d comma 0 less than b to the power of 2 end exponent less than c, then f(x)

If f(x) equals x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d comma 0 less than b to the power of 2 end exponent less than c, then f(x)

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The set of value (s) of a’for which the function f left parenthesis x right parenthesis equals fraction numerator a x to the power of 3 end exponent over denominator 3 end fraction plus left parenthesis a plus 2 right parenthesis x to the power of 2 end exponent plus left parenthesis a minus 1 right parenthesis x plus 2 possess anegative point of inflection‐

The set of value (s) of a’for which the function f left parenthesis x right parenthesis equals fraction numerator a x to the power of 3 end exponent over denominator 3 end fraction plus left parenthesis a plus 2 right parenthesis x to the power of 2 end exponent plus left parenthesis a minus 1 right parenthesis x plus 2 possess anegative point of inflection‐

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The greatest, the least values of the function, f left parenthesis x right parenthesis equals 2 minus square root of 1 plus 2 x plus x to the power of 2 end exponent end root comma x element of left square bracket 21 right square bracket are respectively

Hence the final answer is (2,0)

The greatest, the least values of the function, f left parenthesis x right parenthesis equals 2 minus square root of 1 plus 2 x plus x to the power of 2 end exponent end root comma x element of left square bracket 21 right square bracket are respectively

Maths-General

Hence the final answer is (2,0)

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Suppose that f is differentiable for allx and that f to the power of ’ end exponent left parenthesis x right parenthesis less or equal than 2 for all x If f left parenthesis 1 right parenthesis equals 2 and f(4)=8 then f(2) has the value equal to

Hence f(2)=4 is the suitable option

Suppose that f is differentiable for allx and that f to the power of ’ end exponent left parenthesis x right parenthesis less or equal than 2 for all x If f left parenthesis 1 right parenthesis equals 2 and f(4)=8 then f(2) has the value equal to

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Hence f(2)=4 is the suitable option

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f left parenthesis x right parenthesis equals not stretchy integral subscript blank superscript left parenthesis end superscript left parenthesis 2 minus fraction numerator 1 over denominator 1 plus x to the power of 2 end exponent end fraction minus fraction numerator 1 over denominator square root of 1 plus x to the power of 2 end exponent end root end fraction right parenthesis right parenthesis dxthenfis‐

f left parenthesis x right parenthesis equals not stretchy integral subscript blank superscript left parenthesis end superscript left parenthesis 2 minus fraction numerator 1 over denominator 1 plus x to the power of 2 end exponent end fraction minus fraction numerator 1 over denominator square root of 1 plus x to the power of 2 end exponent end root end fraction right parenthesis right parenthesis dxthenfis‐

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The tangent to the curve 3 x y to the power of 2 end exponent minus 2 x to the power of 2 end exponent y equals 1 at (1,1) meets the curve again at the point‐

The final answer is option B

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The final answer is option B

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