CPM Homework Help : APCALC Problem 3-135

If a function $f$ is increasing, such as the one at right, what must be true about $f^\prime$ ?

Explain your idea using the graph at right.
Use your idea to algebraically determine where $g(x) = 3x^2 − 3x + 1$ is increasing.

Continuous increasing curve, starting in the lower left, changing concavity in third quadrant, passing through the origin, changing concavity in first quadrant, continuing up & right.

Hint:

If $f(x)$ is increasing, then slopes are positive so $f ^\prime(x) > 0$ .

Step 1:

Use the Power Rule to find $f ^\prime(x)$ .

Step 2:

Solve the inequality: $f ^\prime (x) > 0$ .