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Algebra
Pregunta

1. Consider the function \( f \) defined by the eq...

1. Consider the function \( f \) defined by the equation \( f ( x ) = 0.5 x ^ { 2 } \) . a. Sketch the graph of this function, with the scale on your \( x \) -axis going from \( - 1 \) to \( 3 \) . Use a full-size sheet of graph paper so you will be able to get enough detail in part c. b. Label the point \( ( 2,2 ) \) on your graph. c. The points listed here are also on your graph. In each case, draw the secant line connecting the point to \( ( 2,2 ) \) and find the slope of that secant. i. \( ( 0,0 ) \) ii. \( ( 1,0.5 ) \) iii. \( ( 1.5,1.125 ) \) iv. \( ( 1.9,1.805 ) \) 

d. Draw the line that is tangent to your graph at \( ( 2,2 ) \) . Estimate the slope of that tangent line and explain your reasoning. e. Find the derivative of the function \( f \) at the point \( ( 2,2 )\) 

Answer

Solución
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