AS Maths Exponential Question

differentiate to find the gradient at the point, once you have the gradient u can find an equation of the line, shouldnt have a +C so it will go through origin

thanks for the reply!

so f(x)=e^0.2x
f'(x)= 0.2e^0.2x

gradient of tangent when x=5 will be
f'(5)=0.2e^0.2x5 =0.2e

then what??

thanks for the reply!

so f(x)=e^0.2x
f'(x)= 0.2e^0.2x

gradient of tangent when x=5 will be
f'(5)=0.2e^0.2x5 =0.2e

then what??

Construct the equation of the tangent. You have all you need; the gradient, and a point the line passes through.

y is e, x is 5, gradient is 0.2e, now u can find equation. just realised there probably will be a +c

how did you get e as y?

just realised there probably will be a +c

Construct the equation of the tangent. You have all you need; the gradient, and a point the line passes through.

so e=0.2e +c

That's not the equation. If you're inputting values into the equation $y=mx+c$ then you clearly forgot to input the x value.

That's not the equation. If you're inputting values into the equation $y=mx+c$ then you clearly forgot to input the x value.

so e=0.2ex +c

shall i sub in 5

giving e =e+c

Ok, finish it off.

Just to give you the overview of what you're doing (because you seem very unsure of what you need to do or what the next steps should be...); you are interested in constructing the equation of the tangent at $(5,e)$. The equation of this tangent will take the form $y=mx+c$, as usual. You found $m=0.2e$. You next step is to determine what $c$ is. If you can show that it is $c=0$ then that would imply the line passes through the origin... hence answering the question.

Find the derivative of the curve at x=5. That will be the gradient of the tangent to the curve at (5,e). The gradient is 0.2e. Next compute equation of the tangent. The tangent passes through (5,e) , (x,y), m = 0.2e. The equation is y = 0.2ex. To check if the tangent passes through the origin, check if the curve satisfies y = 0 when x = 0, since the coordinates of the origin are (0,0). So we have y = 0.2e(0) = 0. Hence we have (0,0). Thus the tangent goes through the origin.