Calculus Question

Question

Let f(x)=3x4−3x2+5.

(a) Find f′(x).

f′(x) = 

(b) Find the slope of the line tangent to the graph of f at x=2.

Slope at x=2: 

(c) Find an equation of the line tangent to the graph of f at x=2.

Tangent line: y = 

Answer 1

Use the point-slope form.

First get the slope of the line. This is just our derivative that you calculated.

Next get a point that the line goes through. We know the line intersects the graph at x = 2

Thus a point the line goes through is (2, f(2))

Now that you have a point and slope, plug into the point-slope eqn:

y - y₁ = m (x - x₁)

Answer 2

f'(2) is the slope of the tangent at x = 2.

Use point slope form from Algebra 1

(y - f(2)) / (x - 2) = f'(2)