AP Calculus AB Exam Question:
Find the derivative of the function
f(x)=3x2−2x+4Step-by-Step Solution:
To find the derivative of the given function, we can use the power rule of differentiation. According to the power rule, if we have a function of the form f(x)=axn, where a and n are constants, then the derivative of f(x) with respect to x is f′(x)=anxn−1.
So, applying the power rule, let's find the derivative of f(x):
f′(x)=dxd(3x2−2x+4)Using the power rule, we differentiate each term separately:
f′(x)=dxd(3x2)−dxd(2x)+dxd(4)f′(x)=3⋅dxd(x2)−2⋅dxd(x)+dxd(4)Applying the power rule to each term:
f′(x)=3⋅2x2−1−2⋅1x1−1+0f′(x)=6x−2Therefore, the derivative of the function f(x)=3x2−2x+4 is f′(x)=6x−2.