Name: _______________________________
Date: ________________________
2.2 The Product Rule
1. Differentiate each function using two
methods.
i) expand and simplify, and then
differentiate
ii) apply the product rule and then
simplify
a) f(x) = (x – 3)(x – 2)
b) f(x) = (2x + 1)(x – 3)
c) f(x) = (–2x + 3)(x – 4)
d) f(x) = (3x – 4)(2 – x)
2. Use the product rule to differentiate each
function.
a) f(x) = (2x + 3)(5x – 1)
b) g(x) = (5 – x)(3 – 2x)
c) h(t) = (4t – 3)(t – 7)
d) d(t) = (3t2 – 4)(2t + 1)
3. Differentiate.
a) f(x) = (2 + x)(x2 – 3)
b) h(t) = (t2 + 4)(t + 3)
c) g(x) = (1.4x + 4)(x2 – 3)
d) p(u) = (2u + 3)(u2 + 1)
4. Determine f (3) for each function.
a) f(x) = (3x + 4)(2x – 1)
b) f(x) = (2x2 – 1)(x – 3)
c) f(x) = (–3x + 4)(x3 + 3)
d) f(x) = (2x2 + 3)(4 – x2)
5. Determine the equation of the tangent to
each curve at the indicated value.
a) f(x) = (2x + 1)(3x – 2), x = 1
b) g(x) = (x2 – 4)(2x + 3), x = –2
c) h(x) = (x3 – 2)(x + 4), x = 2
d) p(x) = (–3x2 + 1)(x2 – 5), x = –1
…BLM 2-4. .
6. Determine the point(s) on each curve that
correspond to the given slope of the
tangent.
a) y = (2x – 3)(x + 1), m = 7
b) y = (4x – 3)(2x + 5), m = 6
c) y = (4 – x)(2x + 1), m = 3
d) y = (x2 – 1)(2x + 3), m = 10
7. Differentiate.
a) y = (4x2 – x + 2)(x – 3)
b) y = (1 – x2)(x2 + 2x – 3)
c) y = (3x2 – 1)2
d) y = 3x2(2x + 1)(5x – 2)
8. The student council is selling tickets for a
dance. In the past, they have found that if
they charge $8 for tickets they will sell
about 300 tickets. For every $1 increase
in price they sell 50 fewer tickets.
a) Write an equation that models the
council’s revenue, R, as a function of
x, where x represents the number of $1
increases in the price.
b) Use the product rule to determine
R(x) .
c) Evaluate R(2) and interpret its
meaning for this situation.
d) What price will result in the maximum
revenue?
9. a) Determine the point on the curve
f(x) = (1 – 2x)2 where the tangent line
is horizontal.
b) Sketch the curve and the tangent.
10. Use the product rule to differentiate.
a) f(x) = (2x + 1)(x2 – 3)(3x – 2)
b) f(x) = (2x2 – 3)(3x + 5)(x + 1)
11. Given f(x) = (ax + 3)(2x + b), find values
of a and b such that f (x) = 8x – 4.