Let f() = x2 f(X) - f(y) a. Show that - -2 . for all x zy . X-y 2 b. Is this property true for f(X) = ax , where a is a nonzero real number? c. Give a geometrical interpretation of this property d. Is this property true for f(x) = ax37 a. Begin by rewriting the left side of the equation f(x) - f(y) Substitute for f(x) and f(y) in the numerator. x - y Simplify. Now, rewrite the right side of the equation. Find f'(x). f(X) = x- f (x) Take the derivative. x + y Use the previous result to find f X + y x+y Evaluate the derivative at - 2 - and simplify b. Is the property true for f() = ax"? Choose the correct answer below f(x) -f(y) A. No. The right side. f includes a factor of a, but the left side, X - y , does not 2 O B. No. The left side. includes a factor of a, but the right side, F -2 . does not. 1(X) -2and |2 O c. Yes. Both x -y simplify to the same result found above. ()and F X-y O D. Yes. Both x -y simplify to the product of a and the result found above. c. Give a geometrical interpretation. Choose the correct answer below. A. The slope of the secant line between (x,f(x)) and (y,f(y)) is equal to the midpoint of the line segment from (x,f(x)) to (y.f(y))-Question 12 of 24 Let f(x) =x- f(x) - f(y) a. Show that (X + y ] x -y 2 . for all x # y. b. Is this property true for f(x) = ax", where a is a nonzero real number? c. Give a geometrical interpretation of this property. d. Is this property true for f(x) = ax? b. Is the property true for f(x) = ax"? Choose the correct answer below. O A. No. The right side f x + y includes a factor of a, but the left side, f(x) -f() X-y :90 does not. fox) - f( y) O B. No. The left side. X- y , includes a factor of a, but the right side. f'-- , does not! O C. Yes. Both 1() - f(y) and f' 2 simplify to the same result found above. O D. Yes. Both 10) and f' X-y 2 simplify to the product of a and the result found above. c. Give a geometrical interpretation. Choose the correct answer below. O A. The slope of the secant line between (x.f(x)) and (y,f(y)) is equal to the midpoint of the line segment from (x,fox)) to (y.f(y)). B. The slope of the secant line between (x.f()) and (y.f(y)) is equal to the sum of the slopes of the lines tangent to f(x) =x