#### Graph sketching using derivatives in investing

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These values give idea about which way the graph of function will lie in the long term on larger values of x. So, following these general rules, we can sketch graphs for any curve. Polynomial functions occur a lot in calculus, and it is essential to know how to sketch their graphs.

We will look at a function and use the techniques studied above to infer the graph of the function. The general idea is to look for asymptomatic values, where they are going and then find the critical points and draw a graph according to them. We know that the domain of this function is all real numbers. This functions will tend to infinity as we go towards large positive and negative values of x.

That is this function is even, so its graph must be symmetric about the y-axis. Now we know that graph goes to infinity and is symmetrical around the y-axis. Now we just need to know the value of the function at minima. We know that logarithmic functions are inverse of exponential functions. The graph of the exponential function is given below. So we can derive the shape of the graph of log function from the given graph of the exponential function. Now we know that graph goes to positive infinity for larger positive values of x and negative infinity for larger negative values of x.

There is no critical point, that means derivatives change sign remains same and constant throughout. So, we will check the sign. This will never become zero, so there are no critical points. The graph is continuously increasing. Due to the addition of 2 to the exponential function. The whole graph will be shifted two units upwards. Writing code in comment?

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STEP questions may not ask you to draw a graph, but you should always consider whether this might be a useful approach. The "Solutions" file leads you through one possible solution, but some steps will be missing and you will still need to work through the question yourself.

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