Question

Calculate the gradients of the curve at the points where y is given.
y=2x²+3x , y=2
help me pls

Answer 1

$y=2x^2+3x\implies y'=4x+3$

When $y=2$, you have

$2=2x^2+3x\iff 2x^2+3x-2=(2x-1)(x+2)=0\implies x=\dfrac12,-2$

When $x=\dfrac12$, the gradient is $4\times\dfrac12+3=5$.

When $x=-2$, the gradient is $4\times(-2)+3=-5$.