Find the derivative of the function f(x) = 3x + 5.
Answer
f(x) = 3x + 5 has a slope of 3, therefore f ' (x) = 3.
Find the derivative of the function f(x) = 2x.
f(x) = 2x has a slope of 2, therefore f ' (x) = 2.
Find the derivative of the function f(x) where f is the line that passes through the points (4, 5) and (-1, -2).
The line that passes through the points (4, 5) and (-1, -2) has a slope of
therefore
.
Find the derivative of the function f(x) = 4.
f(x) = 4 is a constant function, so its derivative is 0.
Alternately, we can think of the line in slope-intercept form as f(x) = 0x + 4, which we can see has a slope of 0.
Find the derivative of the function f(x) = 7(x – 1) + 3.
f(x) = 7(x – 1) + 3 multiplies out to f(x) = 7x – 4, which has a slope of 7, therefore f ' (x) = 7.
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