# Thread: Sketching cubic function to calculate area under the curve by integration

1. ## Sketching cubic function to calculate area under the curve by integration

Hi,
The question asks us the sketch the curve of y= 3x^3-10 for x E [2,4].

i've tried the usual way of finding interepts. For the y intercept i get the point (0,-10). The x intercept gives me x^3=10/3 which doesn't seem to help me for sketching purposes.

I then tried to find max and mins but when i let dy/dx = I keep getting the same coordinates as for the y intercept. Also tried getting point of inflection but get the same point again. Should I just sub in values for x and get their corresponding y values?

2. ## Re: Sketching cubic function to calculate area under the curve by integration

quite hard to help you without just telling you the answer. do you know what $\displaystyle y=x^3$ looks like?

if you are on a basic course...you could just substitute values of x (say 2,2.5,3,3.5,4) into the function and plot the values.

3. ## Re: Sketching cubic function to calculate area under the curve by integration

Because your question is interested in the particular interval [2,4] , your critical points are x = 2, x=4 and value of x where the d/dy equals 0. The only place d/dy equals zero is at the point x=0, whcih is not in your interval.

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# cubic equation area under the curve

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