Answer:
The two horiz. tang. lines here are y = -3 and y = 192.
Step-by-step explanation:
Remember that the slope of a tangent line to the graph of a function is given by the derivative of that function. Thus, we find f '(x):
f '(x) = x^2 + 6x - 16. This is the formula for the slope. We set this = to 0 and determine for which x values the tangent line is horizontal:
f '(x) = x^2 + 6x - 16 = 0. Use the quadratic formula to determine the roots here: a = 1; b = 6 and c = -16: the discriminant is b^2-4ac, or 36-4(1)(-16), which has the value 100; thus, the roots are:
-6 plus or minus √100
x = ----------------------------------- = 2 and -8.
2
Evaluating y = x^3/3+3x^2-16x+9 at x = 2 results in y = -3. So one point of tangency is (2, -3). Remembering that the tangent lines in this problem are horizontal, we need only the y-coefficient of (2, -3) to represent this first tangent line: it is y = -3.
Similarly, find the y-coeff. of the other tangent line, which is tangent to the curve at x = -8. The value of x^3/3+3x^2-16x+9 at x = -8 is 192, and so the equation of the 2nd tangent line is y=192 (the slope is zero).
Answer:
k = 11
Step-by-step explanation:
k/90 - 1/9 = 1/90
k/90 = 1/90 + 1/9
k/90 = 1 + 10/90
k/90 = 11/90
k = 11/90 / 90
k = 11/90 * 90
k = 11
Answer:
This would shift the equation to the right by 5
Step-by-step explanation:
Answer: it would be g because if you distribute 9, you end up with x+72 and the bottom one is 9•8 (also 72)+x
Answer:
Mckayla 30%
Jacob 30%
Daniel 20%
Samantha 10%
Maria 10%
Step-by-step explanation: First Divide 20% into half to get samantha and marias percent then add those together then subtract what you get from that to 100% and then divide into half for Mckayla and Jacobs percent
