Let f(x) = 4×2. Compute f(3 + h).
(Use symbolic notation and fractions where needed.)
f(3 + h)
=
Compute
f(3+h)-f(3)
h
(Use symbolic notation and fractions where needed.)
f(3+h) – f(3)
h
=
Compute f'(3) by taking the limit as h +0.
(Give your answer as a whole or exact number.)
f(3) =
Let f(x) = 4×2 – 3x – 7. The secant line through (2, f(2)) and (2 +h, f(2 + h)) has slope 4h + 13. Use this formula to
compute the slope of the given lines.
(a) Find the slope of the secant line through (2, f(2)) and (3, f(3)).
(Give your answer as a whole or exact number.)
mi
=
=
(b) Find the slope of the tangent line at x = 2 (by taking a limit).
(Give your answer as a whole or exact number.)
m2
X – 3
f(2)-f(3)
Find the difference quotient
when f(x) = 1 – 3x + 6×2. Simplify the expression fully as if you were going to
compute the limit as x + 3. In particular, cancel common factors of x – 3 in the numerator and denominator if possible.
(Use symbolic notation and fractions where needed.)
f(x) – f(3)
2 – 3
=
Use your result to compute the derivative.
(Give your answer as a whole or exact number.)
f(3) =
Find the equation of the tangent line at (2, f(2)) when f(2) = 6 and f'(2) = 2.
(Use symbolic notation and fractions where needed.)
equation:
Use the limit definition to calculate the derivative at z = a of the linear function k(z) = 15z + 19.
(Give your answer as a whole or exact number.)
k'(a) =
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