(PLEASE HELP ME WITH THESE THREE QUESTIONS) 1.Consider the following function. f
ID: 2871883 • Letter: #
Question
(PLEASE HELP ME WITH THESE THREE QUESTIONS)
1.Consider the following function.
f(x) = |x 9|
Find the derivative from the left at x = 9. If it does not exist, enter NONE.
Find the derivative from the right at x = 9. If it does not exist, enter NONE.
2.Find the slope of the tangent line to the graph of the function at the given point.
g(x) = 11 x2; (3, 2)
(Exact number)
3.Find the equations of the two tangent lines to the graph of f that pass through the indicated point.
f(x) = 6x x2
y =
line with positive slope, y = line with negative slope,y =
Explanation / Answer
1) When x > 9
f(x) = x - 9
f'(x) = 1
When x < 9
f(x) = -x + 9
f'(x) = -1
So the derivative doesn't exist.
2) g(x) = 11 - x^2
g'(x) = -2*x = -2*3 = -6
3) f(x) = 6x - x^2
f'(x) = 6 - 2*x
m = 6 - 2*2 = 2
Let this line be a tangent to the curve
y = 2x + c1
y = 2*x + c1
(3,10) lies on this line
10 = 2 * 3 + c1
c1 = 4
y = 2x + 4
f'(x) = 6 - 2*x
m = 6 - 2*4 = -2
Let this line be a tangent to the curve
y = -2x + c2
(3,10) lies on this line
10 = -2 * 3 + c2
c2 = 16
y = -2x + 16
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