Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# A function f is defined by f:x →x^3-x^2-8x+5 for x<a.its given that f is an increasing function. Find the largest possible value of a?

Relevance
• f(x) = x³ - x² - 8x + 5

f '(x) = 3x² - 2x - 8 = 0...at stationary points

i.e. (3x + 4)(x - 2) = 0

so, at x = -4/3 and x = 2

Hence, we need to examine f '(x) for x < -4/3, -4/3 < x < 2 and for x > 2

For, x < -4/3...i.e. x = -2 we have:

f '(-2) = 3(-2)² - 2(-2) - 8 > 0

for -4/3 < x < 2...i.e. x = 0 we have:

f '(0) = 3(0)² - 2(0) - 8 < 0

for x > 2...i.e. x = 3 we have:

f '(3) = 3(3)² - 2(3) - 8 > 0

so, f(x) is increasing for x < -4/3 and for x > 2

Hence, if x < a...then a = -4/3

See sketch below.

:)> • f(x) = x^3 - x^2 - 8x + 5 See where f is increasing on this graph

https://www.wolframalpha.com/input/?i=y+%3D+x%5E3+...

Differentiate and set to zero to show turning points at x = -4/3 and x = 2

Find the largest possible value of a where f is an increasing function for x<a.

That should now be obvious to you.

• Anonymous
1 month ago

Sorry, but your tewacher wants YOU  to find it. If you don't know how, get a proper tutor.