f(x) = x√(36 − x^2) + c; P(5, 10)

Question

Find the value of c such that the point P(a, b) lies on the graph of the function f.

Answer 1

The first step is to realize that the point (5,10) means that f(x)=10 when x=5 so we just need to plug them into the function and solve for c

10 = 5√(36 - 5²) + c

10 = 5√(36 - 25) + c

10 = 5√(11) + c

10 - 5√(11) = c

since you are in calculus I assume your teacher does not want a decimal so we will leave it as c = 10 - 5√11