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`