CPM Homework Help : CALC Problem 3-28

Find slope functions, f ′(x), for the following functions: Homework Help ✎
1. f(x) = 7x²
2. f(x) = π² (Careful!)
3. f(x) = 2(x − 2)⁴ + 18x

Hint (a):

Use the Power Rule.If f(x)=axⁿ, then f '(x) = naxⁿ⁻¹

Answer (a):

f '(x) = 14x

Hint (b):

Remember that π is just a number, not a variable!

Hint (b):

Since π ≈ 3, what is the slope function of y = 3²? Use that to find the slope function of f(x) = π².

Hint (c):

f(x) is a horizontal shift of y = 2⁴+18x, whose slope function is easy to find with the Power Rule (see hint in part (a)). As for f(x), THINK! Since slopes will shift with the function... f '(x) will equal a shifted version of y '.

Answer (c):

f '(x) = 8(x−2)³+18

Hint (d):

See hint in part (a).