If function f(x) = ax**2 + bx + 1 for x<= 1 and f(x) = ax**3 - 2bx**2 - 5x for x

Question

If function f(x) = ax**2 + bx + 1 for x<= 1 and f(x) = ax**3 - 2bx**2 - 5x for x> 1 and f(x) is differentiable for all x, find a and b I know that we can equate the lim as x-->1+ and x--> -1 as f(x) is differentiable This gives a + b + 1 = a - 2b -5 giving b = -2. Now I am stuck on how to solve for a.

Explanation / Answer

f(x) is differentiable for all x => it is continuous and differentiable at 1. => f(1+)=f(1-) and f'(1) exists. f(1+) = a+b+1 f(1-) = a-2b-5 => b = 2. f'(x) = 2ax+bx for x1 for f'(1) to exist, f'(1+)=f'(1-) f'(1+) = 2a+b = 2a+2 f'(1-) = 3a-4b-5 = 3a-13 => a = 15.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.