Consider the function f(x) = 2/3 x^3 + bx^2 + 2x + 3, where b is some undetermined coefficient:
a) Find f ' (x) and f ''(x). f' = 2x2 + 2bx + 2f'' = 4x + 2bb) You are given that f(x) has a stationary point at x = 2. Use this information to find b.2x2 + 2bx + 2, x=2Stationary point is when f' = 02(2)2 + 2b(2) + 2 = 08 + 4b + 2 = 04b = -10b = -2.5c) Find the coordinates of the other stationary point.2x2 - 5x + 2 = 0(2x−1)(x−2)x = 0.5 or x=2Sub x = 0.5 into original function to get: (0.5 , 83/24)
CP
Related Maths A Level answers
All answers ▸Solve ∫(x+2)/(2x^2+1)^3 dx
How to integrate ln(x)
What is the derivative of f(x)=sqrt(3x+2)=(3x+2)^(1/2)?
The line L1 has vector equation, L1 = ( 6, 1 ,-1 ) + λ ( 2, 1, 0). The line L2 passes through the points (2, 3, −1) and (4, −1, 1). i) find vector equation of L2 ii)show L2 and L1 are perpendicular.