Question

Let f(x)= 3x^2 / (2x+1) . At what value of x does f(x) have a tangent with slope 4/3?

Answer 1

did you find the derivative?

Answer 2

i found the derivative to be \[6x ^{2} + 6x \div (2x+1)^{2 }\]

Answer 3

you should get
\[\frac{6x^2+6x}{(2x+1)^2}\] so solve
\[\frac{6x^2+6x}{(2x+1)^2}=\frac{4}{3}\] via
\[3(2x+1)^2=3(6x^2+6x)\]

Answer 4

ok typo, i meant
\[4(2x+1)^2=3(6x^2+6x)\]

Answer 5

okay thank you!

Answer 6

yw
annoying quadratic, but you can solve it yes?