I need some help on a few problems. If someone can help me I will appreciate it.
1) Determine the dimensions of a rectangle solid(with a square base) with maximum volume if its surface area is 625 meters.
2) Find an equation of the line that is tangent to the graph of function f(x)=11/sqrt(x) and parallel to the line 11x+2y-6=0
3) Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.
y(x)=x^4-4x+9
1) Determine the dimensions of a rectangle solid(with a square base) with maximum volume if its surface area is 625 meters.
2) Find an equation of the line that is tangent to the graph of function f(x)=11/sqrt(x) and parallel to the line 11x+2y-6=0
3) Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.
y(x)=x^4-4x+9
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1.It'll be a cube. If the surface area is 625, then each face will be 625/6 sq. m, and the edge is 25/√6.
2. 2y = -11x + 6 ==> slope is -11/2. For f(x) = 11 x^(-1/2), f'(x) = -11/2 x^(-3/2) = -11/2 ==> x^(-3/2) = 1 ==> x = 1 ==> f(1) = 11
y - 11 = -11/2 (x - 1) (Answer)
3. y = x^4 - 4x + 9 ==> dy/dx = 4x^3 - 4 = 0 ==> x^3 = 1 ==> x = 1 (Answer)
2. 2y = -11x + 6 ==> slope is -11/2. For f(x) = 11 x^(-1/2), f'(x) = -11/2 x^(-3/2) = -11/2 ==> x^(-3/2) = 1 ==> x = 1 ==> f(1) = 11
y - 11 = -11/2 (x - 1) (Answer)
3. y = x^4 - 4x + 9 ==> dy/dx = 4x^3 - 4 = 0 ==> x^3 = 1 ==> x = 1 (Answer)