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Maths-

General

Easy

Question

Any tangent to the curve $y equals 2 x to the power of 5 end exponent plus 4 x to the power of 3 end exponent plus 7 x plus 9$

Is parallel to $x$ -axis
Is parallel to $y$ -axis
Makes an acute angle with the $x$ -axis
Makes an obtuse angle with $x$ -axis

The correct answer is: Makes an acute angle with the $x$ -axis

We have,
$y equals 2 x to the power of 2 end exponent plus 4 x to the power of 3 end exponent plus 7 x plus 9$

$rightwards double arrow fraction numerator d y over denominator d x end fraction equals 10 x to the power of 4 end exponent plus 12 x to the power of 2 end exponent plus 7 greater than 0$ for all $x element of R$

Thus, any tangent to the given curve makes an acute angle with $x$ -axis

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