Question

Let f be a differentiable function such that f(4)=7 and f′(4)=15. The graph of f is concave up on the interval (3,5). Which of the following is true about the approximation for f(3.5) found using the line tangent to the graph of f at x=4 ?

Answer 1

since f is concave up on (3,5)
f' is increasing on (3,5)
So, since the tangent line has constant slope, the graph of f will curve up away from the tangent line, making the estimate lower f(x) on the interval.