Question
Consider the graph of the parabola f(x)equals=x squaredx2. For xgreater than>0 and hgreater than>0, the secant line through (x,f(x)) and (xplus+h,f(x+h)) always has a greater slope than the tangent line at (x,f(x)).
Choose the correct answer below.
A.
The statement is true. Since the slope of x squaredx2 is increasing for xgreater than>0, the average rate of growth on the interval [x,xplus+h] is greater than the instantaneous rate of growth at x.
B.
The statement is true. The slope of the secant line through (x,f(x)) and (xplus+h,f(xplus+h)) is left parenthesis x plus h right parenthesis squared(x+h)2, which is greater than x squaredx2, the slope of the tangent line at (x,f(x)).
C.
The statement is false. The tangent line at (x,f(x)) is the limit of secant lines through (x,f(x)) and (xplus+h,f(xplus+h)) as h goes to zero.
D.
The statement is false. If x and h both equal 1, then the tangent line at point (1,1) and the secant line through (1,1) and (2,4) have the same slope.
Choose the correct answer below.
A.
The statement is true. Since the slope of x squaredx2 is increasing for xgreater than>0, the average rate of growth on the interval [x,xplus+h] is greater than the instantaneous rate of growth at x.
B.
The statement is true. The slope of the secant line through (x,f(x)) and (xplus+h,f(xplus+h)) is left parenthesis x plus h right parenthesis squared(x+h)2, which is greater than x squaredx2, the slope of the tangent line at (x,f(x)).
C.
The statement is false. The tangent line at (x,f(x)) is the limit of secant lines through (x,f(x)) and (xplus+h,f(xplus+h)) as h goes to zero.
D.
The statement is false. If x and h both equal 1, then the tangent line at point (1,1) and the secant line through (1,1) and (2,4) have the same slope.
Answers
Steve
while the tangent line is the limit of the secants lines, that was not the question. It said h > 0.
Draw a parabola. The secants are always steeper than the tangents.
So, (A)
Draw a parabola. The secants are always steeper than the tangents.
So, (A)