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Maths-

General

Easy

Question

If the normal to the curve $y equals f left parenthesis x right parenthesis$ at the point (3, 4) makes an angle $fraction numerator 3 pi over denominator 2 end fraction$ with the positive $x$ -axis, then $f to the power of ´ end exponent left parenthesis 3 right parenthesis$ is equal to

$- 1$
$- \frac{3}{4}$
$\frac{4}{3}$
1

The correct answer is: 1

Slope of the curve at an angle $theta equals fraction numerator 3 pi over denominator 4 end fraction$ is
$fraction numerator d y over denominator d x end fraction equals tan invisible function application fraction numerator 3 pi over denominator 4 end fraction equals negative 1$

Slope of the normal $equals fraction numerator negative 1 over denominator d y divided by d x end fraction$

$therefore blank open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript open parentheses 3 comma blank 4 close parentheses end subscript equals 1$

$rightwards double arrow blank f to the power of ´ end exponent open parentheses 3 close parentheses equals 1$

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