Question

5. The gradient of the tangent line to the graph of f(x)= 2x^2 + kx - 3 at x = -1 is 1. Find the value of k

Answer 1

The gradient of the tangent line to $y(x)$ at $(c,y(c))$ is given by the value of the derivative at $x=c$. We have

$f(x)=2x^2+kx-3\implies f'(x)=4x+k$

We're told that $f'(-1)=1$. Then

$1=4(-1)+k\implies k=5$