Find the equation of the line tangent to the graph of f at the indicated value of x.
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A) y = 2ex - 4e + 1
B) y = 2ex + 4e + 1
C) y = 2ex + 1
D) y = 4ex - 1

Question

Find the equation of the line tangent to the graph of f at the indicated value of x.
-
A) y = 2ex - 4e + 1 
B) y = 2ex + 4e + 1 
C) y = 2ex + 1 
D) y = 4ex - 1

Quizplus · Accepted Answer

Taking the derivative of f(x) = 2ex - x + 1, we get f'(x) = 2ex - 1. 
Plug in x = 0 to find the slope of the tangent line: f'(0) = 2(1) - 1 = 1. 
Using the point-slope form of the equation of a line: y - f(0) = f'(0)(x - 0)
y - 2 = 1(x - 0)
y = x + 2
But we need to express the equation in terms of e. 
Substitute e^x for x to get y = e^x + 2. 
This matches choice C.

Find the Equation of the Line Tangent to the Graph