Given y = x^3 + 4x + 1, find the value of dy/dx when x=3
To differentiate this equation, you must bring the power of each x term down to the front and reduce the power of x by 1, with constants disappearing:
dy/dx = 3x3-1 + (41)*x1-1 = 3x2 + 4
To find the value of this when x=3, simply substitute this value into the equation for dy/dx:
dy/dx = 3(3)2 + 4 = 27 + 4 = 31
This value represents the gradient of the line y = x3+4x+1 when x=3.
FH
Related Maths A Level answers
All answers ▸What's the point of Maths?
Find the intersection points between the graphs y=2x+5 and y=x^2-9.
Solve the differential equation: dy/dx = 6x^2 + 4x + 9
f(x)=(2x+1)/(x-1) with domain x>3. (a)Find the inverse of f(x). (b)Find the range of f(x). (c) g(x)=x+5 for all x. Find the value of x such that fg(x)=3.