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Dima020 [189]
3 years ago
11

Suppose f(x) is continuous on [2,8] and −4≤f′(x)≤5 for all x in (2,8). Use the Mean Value Theorem to estimate f(8)−f(2).

Mathematics
1 answer:
bazaltina [42]3 years ago
6 0
<span>2≤x≤8</span> <span>−4≤<span>f′</span>(x)≤5</span> f is continuous in differentable on [2,8] so we know there is c btw 2 and 8 such that <span><span>f′</span>(c)=<span><span>f(8)−f(2)</span><span>/8−2</span></span></span> And we know <span>−4≤<span>f′</span>(c)≤5</span> => we have <span>−4≤ <span><span>f(8)−f(2)</span><span>/8−2</span></span> ≤<span>5</span></span>
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