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# A calculus problem

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Estimate the instantaneous rate of change for the function f(x)=e^x at x=0, then use this to find an equation for the tangent line.  Check your answer by graphing the function and it's tangent line in Desmos.  Print out and attach a copy of your graph.

I have a worksheet in my calculus class due on Monday, April 9, 2018 and need help with this question.  Anyone who knows the answer and can show step-by-step instructions, I would really appreciate it.  Thanks.

Apr 9, 2018

#1
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Estimate the instantaneous rate of change for the function f(x)=e^x at x=0, then use this to find an equation for the tangent line.  Check your answer by graphing the function and it's tangent line in Desmos.  Print out and attach a copy of your graph.

f(x)=e^x

f'(x)=e^x

f'(0)=e^0=1

So the instantaneous rate of change at x=0 is 1, this is also the gradient of the tangent to the curve at x=0 as that is what the instantaneous rate of change IS

When x=0

f(0) = e^0 = 1

so what is the equation of the line through (0,1) with a gradient of 1

y=mx+b

y=1x+1

y=x+1

You can do the desmos graph I expect :)

Apr 9, 2018
#3
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Thanks for the help.  I way over thought this problem. y=mx+b makes total sense.  I feel really dumb.  Now I can finish my homework.  I do know how to use Desmos.

gibsonj338  Apr 9, 2018
#2
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Estimate the instantaneous rate of change for the function f(x)=e^x at x=0, then use this to find an equation for the tangent line.  Check your answer by graphing the function and it's tangent line in Desmos.  Print out and attach a copy of your graph.   Apr 9, 2018