Consider the following function: f(x) = 15x^2 + 2x^3 - x^4. a) Is f(x) is even?

Question

Consider the following function: f(x) = 15x^2 + 2x^3 - x^4. a) Is f(x) is even? Odd? What symmetry will the graph have? b) Graph f(x) neatly and accurately on [-3, 5, 1, 0, 150, 30]. c) Use your calculator to find the two local maximums. d) Use your calculator to approximate the area under the curve on [-3, 5]. e) Find the slope of the line between (- 2, f(-2)) and (4, f(4)). Explain what this slope means. Consider the "direction" and "steepness" of the curve. f) Find the slope of the line between (x, f(x)) and (x + h, f (x + h)). SimpUfy the fraction. g) Visit wolframalpha.com to only verify your numerator in part (f).

Explanation / Answer

f . Slope of the line jioning the 2 points : m = [ f ( x+h ) - f(x) ] /(x+h-x)

= [ f(x+h) - f(x) ] / h the value depends on ' h ' when 'h ' --.>0

if the limit exist then this ratio is called derivative of f(x) at the point x

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