(11) Let f(x) = x^3− 1 and g(x) = 2 + 5 sin 3x. (a) What is the range of g(f(x))? Justify your answer.
(b) If h(x) = f(g(x)) compute h′(x).
(c) If t(x) = e^f(x) compute t′(x). [6 marks]
(d) Obtain f′(x) from first principles. [6 marks]
(e) Obtain the equation of the line tangent to the curve y = f(x) at x = 3.

where is the figure

answer:   rotate 270° clockwise about (7, 1) and reflect across the line x = 7

step-by-step explanation:

because i took test

table a is wierd

step-by-step explanation:

6*f

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)