Difference between revisions of "009A Sample Final 1, Problem 6"

Revision as of 20:47, 1 February 2016

Consider the following function:

f(x)=3x-2\sin x+7

a) Use the Intermediate Value Theorem to show that $f(x)$ has at least one zero.

b) Use the Mean Value Theorem to show that $f(x)$ has at most one zero.

Foundations:

Solution:

(a)

(b)

Step 2:

Step 3:

(c)

Step 1:

@@ Line 3: / Line 3: @@
 ::::::<math>f(x)=3x-2\sin x+7</math>
-::<span class="exam">a) Use the Intermediate Value Theorem to show that <math>f(x)</math> has at least one zero.
+<span class="exam">a) Use the Intermediate Value Theorem to show that <math>f(x)</math> has at least one zero.
-::<span class="exam">b) Use the Mean Value Theorem to show that <math>f(x)</math> has at most one zero.
+<span class="exam">b) Use the Mean Value Theorem to show that <math>f(x)</math> has at most one zero.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"