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 ▸Calculate dy/dx for y=x(x−1)
Show that the derivative of tan(x) is sec^2(x), where sec(x) is defined as 1/cos(x). [Hint: think of tan(x) as a quotient of two related functions and apply the appropriate identity]
a curve has an equation: y = x^2 - 2x - 24x^0.5 x>0 find dy/dx and d^2y/dx^2
b) The tangent to C at P meets the coordinate axes at the points Q and R. Show that the area of the triangle OQR, where O is the origin, is 9/(3-e)