Use the given graph to estimate the value of each derivative. Then sketch the graph of \(f \prime\)

(a) \(f^{\prime}(-3)\)

(b) \(f^{\prime}(-2)\)

(c) \(f^{\prime}(-1)\)

(d) \(f^{\prime}(0)\)

(e) \(f^{\prime}(1)\)

(f) \(f^{\prime}(2)\)

(g) \(f^{\prime}(3)\)

Step 1 of 4

The value of the derivative at any x value by drawing the tangent point and then estimating its slope. The slope is the y-value on the graph of f’.

By the observation, at the value of the slope is can be calculated by the ratio of the rise and the run which is equal to and is decreasing at.

Therefore, the value of the derivative is.

Similarly, the tangent at is horizontal.

The value of the derivative at is

At, the rise if half than the run and is increasing.

Therefore, the value of the derivative is