Graph is f questions are to find with h(x)=g(3x)

Question

Graph of f: https://us-static.z-dn.net/files/d5d/53c5936d080f0d9eaf90caac5fae33ad.jpg

Questions: https://us-static.z-dn.net/files/d56/8b35873b43ef56be3a29f8c22aed2061.jpg

Answer 1

If you work out the whole exercise, you'll find g(6) = 0.

a) lim x→2 h(x)/(x-2) = lim x→2 ∫₂^3xf(t)/dt /(x-2) gives 0/0 so we can use L'Hopital

So, lim x→2 f(3x)/1 = f(6) = -4

b) y=h'(x)(x-x₁)+h(x)

h(1) = ∫₂³f(t)dt = 3 by observing and adding shape areas for [2,3]

h'(x) = d/dt∫₂^3xf(t) dt = f(3x) by ftc

h'(1)= f(3) = 2

y = 2(x-1)+3 = 2x-1

c) h'(0) = f(0) = 4