Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

If the function below is differentiable at x=3, find a+b

[tex]\left \{ {ax+b, x\ \textless \ 3} \atop {x^2-4x+8, x\geq 3}} \right.[/tex]

Sagot :

Answer:

a+b=1

Step-by-step explanation:

y = x² - 4x + 8   .... y = 3² - 4*(3) + 8 = 5

(3,5) is tangent point and function is differentiable at x=3

dy/dx 2x - 4 = 0

x=2  .. slope of tangent

ax + b must continuous to function x² - 4x + 8 at (3,5) and its slope=2

(y-5)/(x-3) = 2

y-5 = 2x - 6

y = 2x - 1 = ax +b

a = 2 and b = -1

a + b = 2 + -1 = 1

View image lynnkc2000
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.