Answer to Question #177681 in Math for John

Question

Differentiate y with respect to x and hence find the gradient of the tangent to the curve

y=4x²+ 3x+2  when x =2.

Answer 1

$$y'=(4x^2+3x+2)'=8x+3$$

$$y'(2)=8(2)+3=19$$

$y'=8x+3$

The gradient of the tangent to the curve $y=4x^2+3x+2$ when $x=2$ is $19.$