Slope at a point

Question

What is the slope for the function y = -5x^2 + 2 at the point x=1

1) -5

2) -10

3) -3

4) The slope cannot be determined

Answer 1

Since the slope at a point is the value of the derivative at that point, we need to find the derivative:

y = -5x² + 2

y' = -5(2)x = -10x

At x = 1

y' (1) = -10(1) = -10

The slope is -10.

Answer 2

y = -5x² + 2

dy/dx = -10x

Slope when x = 1 is -10(1) = -10