Question

Find the slope of the curve y= 1/3x^2−2x+15 at the point (5,7).

a) -1
b) 0
c) 1
d) 2

Answer 1

The slope of the curve y = 1/3x^2 - 2x + 15 at the point (5,7) is 4/3.

Step-by-step explanation:

To find the slope of the curve y = 1/3x^2 - 2x + 15 at a specific point, we need to take the derivative of the function, which gives us the slope of the tangent at any point x. The slope of a curve at a given point can be found by taking the derivative of the equation of the curve with respect to x. In this case, the equation of the curve is y = (1/3)x^2 - 2x + 15.

Taking the derivative of this equation gives dy/dx = (2/3)x - 2.

Substituting x = 5 into the derivative equation gives dy/dx = (2/3) * 5 - 2 = 10/3 - 2 = 4/3.

Therefore, the slope of the curve at the point (5,7) is 4/3.