# math calculus

posted by .

Find the equation of the function f whose graph passes through the point (0, 4/3) and whose derivative is

f'(x) = x sqrt 16 − x^2
.

f(x) =

• math calculus -

Did you mean

f'(x) = x√(16-x^2) ??? , brackets are needed here.

then f(x) = (-1/3)(16 - x^2)^(3/2) + c
(differentiate to confirm)

if x = 4/3 , f(4/3) = 0

0 = (-1/3)(16 - 16/9)^(3/2) + c

solve for c and sub back into f(x) =

## Similar Questions

1. ### calculus

The function f is defined by f(x) = x^3 - x^2 - 4x + 4 The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0, -8) which is not on the graph of f. Find the values of a and b. I have …
2. ### Math

1. Write a quadratic function in intercept form whose graph has the given x-intercepts and passes through the given point. x-intercepts: 2,3 point: (4,2) 2. Write a quadratic function in standard form whose graph passes through the …
3. ### Math-Logarithmic function

Find the equation of a logarithmic function whose graph has x-intercept 8, a vertical asymptote at x=0, and which passes through the point (1/2,4)
4. ### Math-Logarithmic function

Find the equation of a logarithmic function whose graph has x-intercept 8, a vertical asymptote at x=0, and which passes through the point (1/2,4)
5. ### math

find the exponential function of the form y=ab^x whose graph passes through the points (4,6) and (7,10) i got a=3.04 and b= 1.185 so my equation is y=3.04(1.185)^4 is this correct?
6. ### algebra

3. write the function whose graph is the graph of y=sqrt of x, but is shifted to the left 3 units y=____ 4. write the function whose graph is the graph of y=|x|, but is shifted down 8 units y=___ 5. write the function whose graph is …
7. ### math calculus

Find the equation of the function f whose graph passes through the given point. (Remember to use ln |u| where appropriate.) f'(x) = x^3 − 4x^2 + 3/ x − 3 ; (4, −5) f(x) =
8. ### Calculus

Sketch a graph of the parabola y=x^2+3. On the same graph, plot the point (0,−6). Note there are two tangent lines of y=x2+3 that pass through the point (0,−6). The tangent line of the parabola y=x^2+3 at the point (a,a^2+3) …
9. ### Calculus-Mean Value Theorem

Find the function G(x) whose graph passes through (pi/38,-12)and has f(x) as its derivative: G(x)= I already found which is: F(x)=76(1/-19)cos(19x)+C
10. ### Algebra

Find the equation of the line, in slope-intercept form, that satisfies the given conditions. The graph is perpendicular to the graph of y = 5x − 9 and passes through the point whose coordinates are (3, −1).

More Similar Questions