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.