If the value of maximum slope of fx=-x3+8x2-13x-18 is λ, then the value of 3λ5 must be - Maths - Application of Derivatives

Question

If the value of maximum slope of f x = - x 3 + 8 x 2 - 13 x - 18
  is   λ , then the value of 3 λ 5 must be

Aarushi Mishra · Accepted Answer

Slope is given by f'xfx=-x3+8x2-13x-18f'x=-3x2+16x-13Let f'x=gxWe need to find the maximum value of gxNowg'x=-6x+16g'x=0-6x+16=0-3x+8=0x=83g''x=-6<0Hence gx will have maximamax gx=g83=-3832+1683-13=-3649+1683-13=-643+1283-13=643-13=64-393=253So, λ=2533λ5=35×253=5

If the value of maximum slope of f x = - x 3 + 8 x 2 - 13 x - 18 is λ , then the value of 3 λ 5 must be

If the value of maximum slope of $f (x) = - x^{3} + 8 x^{2} - 13 x - 18 is λ$ , then the value of $\frac{3 λ}{5}$ must be