Question

The graph of f’ is shown above. The points (2,6)(2,6) and (4,18)(4,18)are on the graph of f. Which of the following is an equation of the line tangent to the graph of f at x=2?

Answer 1

Answer: y = 5x-4

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Explanation:

The point (2,5) is on the f ' (x) graph. This means x = 2 and f ' (x) = 5.

The slope of the tangent line is m = 5 when x = 2.

We are told that the point (2,6) is on the f(x) curve. So x = 2 and y = 6

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Use m = 5, x = 2, y = 6 to find the value of b

y = mx+b

6 = 5*2+b

6 = 10+b

10+b = 6

b = 6-10

b = -4

The equation of the tangent line at x = 2 is therefore y = 5x-4