Question

Find the slope of the tangent to y=x³+5x+2 at (2,20).

Answer 1

Answer:

$\text{slope of tangent }=17$

Step-by-step explanation:

Find the slope of the tangent to y=x³+5x+2 at (2,20).

Given curve is

$y=x^3+5x+2$

Differentiate with respect to 'x'

$\frac{dy}{dx}=3x^2+5$

$\text{slope of tangent }\:m=(\frac{dy}{dx})_(2,20)$

$\implies\:m=3(2)^2+5$

$\implies\:m=12+5$

$\implies\:m=17$

$\therefore\boxed{\text{slope of tangent }=17}$