Question

The gradiant y=2x³-5x+1 at point (2,7)​

Answer 1

Given:

The equation of the curve is:

`y=2x^3-5x+1`

To find:

The gradient (slope) of the given curve at point (2,7).

Solution:

We have,

`y=2x^3-5x+1`

Differentiate the given equation with respect to x.

`y=2(3x^2)-5(1)+(0)`

`y'=6x^2-5`

Now we need to find the value of this derivative at (2,7).

`y'_((2,7))=6(2)^2-5`

`y'_((2,7))=6(4)-5`

`y'_((2,7))=24-5`

`y'_((2,7))=19`

Therefore, the gradient (slope) of the given curve at point (2,7) is 19.