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=\frac12,-2`

When
`x=\frac12`, the gradient is
`4*\frac12+3=5`.

When
`x=-2`, the gradient is
`4*(-2)+3=-5`.