Solutions to the red boxes please Consider the functionx²+2x-1 if x-1f(x)=√√8x2x+43if 1<<1if x 1(a) To determine whether of is differentiable at x = -1, we computelimh→0+2/3ƒ(−1 + h) − f(−1)h=limh→0+limh→0-0f(-1+h) − f(-1)h=limh→0-(b) To determine whether f is differentiable at x =limh→0f(h) - f(0)hlimh→0(c) To determine whether f is differentiable at x =limh→0+f(1+ h) − f(1)hf(1+h) − f(1)-= lim 2h/3/hh→0+limh→0-hlimh→0-(), we compute1, we compute(d) Classify the differentiability of f at each of the points.f is differentiable at x=a1. x=1f has a vertical tangent line at x=a 2. x = 0f has a cusp at x=a3. x = -1=2/3= 2/3

Consider the function x²+2x-1 if x ≤ -1 f(x) = 3/8x if 1< x < 1 2x+4 if x 1 3 -1, we compute (a) To determine whether f is differentiable at x=-1 lim h→0+ 2/3 f(−1 + h) − f(−1) h - = lim h→0+ lim h→0- 0 ƒ(−1 + h) − f(−1) h = lim h→0- (b) To determine whether f is differentiable at x = 0), we compute lim h→0 f(h) — f(0) h lim 0+4 (c) To determine whether f is differentiable at x = 1, we compute lim h→0+ lim h→0- ƒ(1+ h) − f(1) h f(1+h) − f(1) h - = lim 2h/3/h h→0+ = lim h→0- (d) Classify the differentiability of f at each of the points. f is differentiable at x=a 1. x = 1 f has a vertical tangent line at x=a 2. x = 0 f has a cusp at x=a 3. x=-1 = 2/3 = 2/3