Question

The slope of the tangent to the curve y = x3 - 5x at x = 2 is
(A) 7
(B) 9
(C) 11
(D) None of these​

Answer 1

$\textbf{Given:}$

$\textsf{Curve is}\;\mathsf{y=x^3-5x}$

$\textbf{To find:}$

$\textsf{Slope of tangent of the curve at x=2}$

$\textbf{Solution:}$

$\mathsf{Consider,}$

$\mathsf{y=x^3-5x}$

$\textsf{Differentiate with respect to 'x'}$

$\mathsf{\dfrac{dy}{dx}=3x^2-5}$

$\textsf{Now}$

$\textsf{Slope of tangent at x=2}$

$\mathsf{=\left(\dfrac{dy}{dx}\right)_{x=2}}$

$\mathsf{=3(2)^2-5}$

$\mathsf{=3(4)-5}$

$\mathsf{=12-5}$

$\mathsf{=7}$

$\implies\boxed{\mathsf{Slope\;of\;tangent=7}}$

$\textbf{Answer:}$

$\mathsf{Option\;(A)\;is\;correct}$

$\textbf{Find more:}$

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