A curve with equation y = f(x) passes through the point (4,25). Given that f'(x) = (3/8)*x^2 - 10x^(-1/2) + 1, find f(x).

f'(x) = (3/8)x^2 - 10x^(-1/2) + 1Each term must be integrated (increase the power by 1 and divide by the new power), remembering to include + c.f(x) = (3/8)(x/3)^3 - 10*(2x)^(1/2) + x + cf(x) = (1/8)x^3 - 20 x^(1/2) + x + c = ySubstitute the given values for x and y into the equation, rearrange to find c.25 = (1/8)4^3 - 20 4^(1/2) + 4 + c c = 53Therefore f(x) = (1/8)*x^3 - 20x^(1/2) + x + 53

OW
Answered by Oliver W. Maths tutor

7917 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How can I find the area under the graph of y = f(x) between x = a and x = b?


Express 3 cos θ + 4 sin θ in the form R cos(θ – α), where R and α are constants, R > 0 and 0 < α < 90°.


For y = 7x - x^3, find the two stationary points and what type of stationary points they are.


y = 2x^3 + 15x^2 + 24x + 10 Find the stationary points on this curve and determine their nature


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences