Question

find the slope of the curve y = x3-x2+x at x=2​

Answer 1

Given equation of curve,

$y = {x}^{3} - {x}^{2} + x$

differentiate y with respect to x

we get,

$\frac{dy}{dx} = 3 {x}^{2} - 2x + 1$

this is the slope of tangent at the curve.

Now, slope of tangent at curve at x=2

$( \frac{dy}{dx} )at \: x = 2 \: \: \: = 3( {2}^{2} ) - 2(2) + 1 \\ \\ = 3 \times 4 - 4 + 1 \\ = 12 - 4 + 1 \\ = 9$

Hence,

slope of tangent at curve at x=2 is 9

hope this will help u.