(Solved): Consider the function f(x)=4xx2 and the point P(1,3) on the graph of f. (a) Graph f and the sec ...

Consider the function $$f(x)=4x?x^2$$ and the point $$P(1,3)$$ on the graph of $$f$$. (a) Graph $$f$$ and the secant lines passing through $$P(1,3)$$ and $$Q(x,f(x))$$ for $$x$$-values of $$2,1.5,0.5$$. Find the slope of each secant line. line passing through $$Q(2,f(x))$$ line passing through $$Q(1.5,f(x))$$ line passing through $$Q(0.5,f(x))$$ (b) Use the results of part (a) to estimate the slope of the tangent line to the graph of $$f$$ at $$P(1,3)$$. Describe how to improve your approximation of the slope. Define the secant lines with points farther away from $$P$$. Choose secant lines that are nearly vertical. Choose secant lines that are nearly horizontal. Define the secant lines with points closer to $$P$$.