Given that dy/dx=6-8x+x^4 and that x=1 when y=4. Find an expression for y in terms of x.
Fristly, we should integrate the whole equation,
y=∫ 6-8x+x^4 dx
y=6x-4x^2+x^5/5+C
Then, subsitituting values to find the C,
4=61-41^2+1^5/5+C
4=6-4+1/5+C
4=11/5+C
So, C=9/5.
Hence, y=6x-4x^2+x^5/5+9/5.
PL
Related Maths A Level answers
All answers ▸Solve the following simultaneous equations y + 4x + 1 = 0, y^2 + 5x^2 + 2x = 0
How do you find the gradient of a line at a certain point when f(x) is in the form of a fraction, where both the numerator and denominator are functions of x?
I can differentiate exponentials (e^x), but how can I differentiate ln(x)?
The curve C has equation: (x-y)^2 = 6x +5y -4. Use Implicit differentiation to find dy/dx in terms of x and y. The point B with coordinates (4, 2) lies on C. The normal to C at B meets the x-axis at point A. Find the x-coordinate of A.