a. for f(x) = 2x^5 + 3x^3 + x, find f'(x)
b. how can you use answer to part (a) to determine if f(x) is invertible.
2006-10-01 17:46:27 · 4 answers · asked by ? 1 in Science & Mathematics ➔ Mathematics
a. We can go term by term because there are no multiplications so
f'(x) = 2(5)*x^4 +3(3)*x^2 +1 = 10x^4 + 9x^3 +1
b. by descartes rule of signs there are no zeros of the derivative so if the derivative never goes to zero the slope is either always positive or always negative so the function can never turn back on itself which would make its inverse not a function.
2006-10-01 17:50:41 · answer #1 · answered by Joel D 2 · 0⤊ 0⤋
f(x) = 2x^5 + 3x^3 + x
f'(x) = 10x^4 + 9x^2 + 1
b. by using the power rule, which is [x^n = nx^n-1], and the sum rule, adding term by term.
2006-10-03 04:43:18 · answer #2 · answered by jlpman5000 2 · 0⤊ 0⤋
f'(x) = 10x^4 + 9x^2 + 1
Presence of all even powered terms implies invertibility.
2006-10-01 17:55:09 · answer #3 · answered by ag_iitkgp 7 · 0⤊ 0⤋
integrate f
integral=2 * x^6 / 6 + 9 * x^2 + 1
2006-10-01 17:51:23 · answer #4 · answered by iyiogrenci 6 · 0⤊ 0⤋