What is the gradient of the curve

y= 3e^x - 3 where it crosses the y-axis?
Find the equation of the tangents to the curve at this point.

Question

What is the gradient of the curve

y= 3e^x - 3 where it crosses the y-axis?
Find the equation of the tangents to the curve at this point.

amistre64 · Answer

gradient has a few different meanings; but most likely you want the slope of the line in the xy plane for the equation right?

amistre64 · Answer

2 things we need to determine this

the derivative of the equation with respect to x; and the value of the equation when x=0; (0,f(0))

anonymous · Answer

so first thing we need to find dy/dx

dy/dx=3e^x

at y axis x =0

3*e^0

gradient =3

precal · Answer

Americans say "slope", British say "gradient"

anonymous · Answer

american say rise/run :P

anonymous · Answer

americans*

anonymous · Answer

haha! thanks and what about the second question?

anonymous · Answer

Find the equation of the tangents to the curve at this point.

anonymous · Answer

now plug x=0 in the equation and you will get y=0 

gradient of tangent is also 3

applying formula

y-0=3(x-0)

y=3x

anonymous · Answer

good night fellows Tc. going to study Chemistry now and my CIES are starting from 8th May wish me luck. take care!