Posted by **Yoona** on Tuesday, January 3, 2012 at 2:50am.

5. Let for and f(x)=12X^2 for x>=0 and f(x)>=0

a. The line tangent to the graph of f at the point (k, f(k)) intercepts the x-axis at x = 4. What is the value of k?

b. An isosceles triangle whose base is the interval from (0, 0) to (c, 0) has its vertex on the graph of f. For what value of c does the triangle have a maximum area? Justify your answer.

- calculus -
**Reiny**, Tuesday, January 3, 2012 at 9:58am
dy/dx = 24x

at (k, 12k^2)

dy/dx = 24k

equation of tangent:

y - 12k^2 = 24k(x-k)

but the point (4,0) is on this line

0-12k^2 = 24k(4-k)

-12k^2 = 96k - 24k^2

12k^2 - 96k = 0

k(k-8) = 0

k = 0 or k = 8

at k=0, the tangent would be the x-axis itself, which does pass through the point (4,0)

More than likely they want k=8

check:

if k=8 , the point on the curve is (8, 768)

slope of tangent is 96

tangent equation at (8,768) is

y - 768 = 96(x-8)

for x-intercept, let y = 0

-768 = 96x - 768

0 = 96x

x = 0

- 2nd part - calculus -
**Reiny**, Tuesday, January 3, 2012 at 11:19am
If the base is form (0,0) to (c,0) and the vertex of the isosceles triangle lies on y = 12x^2, then the altitude must right-bisect the base

So if we let the vertex be (a,12a^2) then the base will be on (0,0 and (2a,0)

Area = (1/2)(2a)(12a^2) = 12a^3

As a gets larger, 12a^3 gets larger and there is no maximum area.

## Answer This Question

## Related Questions

- Calculus - Consider line segments which are tangent to a point on the right ...
- Calculus AB - Sorry but I've got a lot of problems that I don't understand. 1) ...
- calculus - Consider line segments which are tangent to a point on the right half...
- Calc. - Find the area of the region bounded by the parabola y=x^2, the tangent ...
- Calculus - Line l is tangent to the graph of y= x - x²/500 at point Q & it ...
- calculus - Let g be a function that is defined for all x, x ? 2, such that g(3...
- Calculus - Given the function defined as f(x)=x^3-(3/2)x^2-6x+10 a) Explain why ...
- Calculus - Given the function defined as f(x)=x^3-(3/2)x^2-6x+10 a) Explain why ...
- Math- calculus - Given f(x) = x ^ 3 - x ^ 2 -4x +4 Find the zeros of f. Write an...
- Calculus - 1. Given the function f defined by f(x) = x^3-x^2-4X+4 a. Find the ...

More Related Questions