Find the values of b such that the function has the given maximum or minimum val

foass77W

foass77W

Answered question

2021-09-15

In order for the function to have the specified maximum or minimum value, find the values of b.
f(x)=x2+bx75 
Maximum value: 25

Answer & Explanation

Talisha

Talisha

Skilled2021-09-16Added 93 answers

Rewriting the equation in standard form will help f(x)=a(xh)2+k 
f(x)=x2+bx75 
=(x2bx)75 We grouped terms and extracted - sign. 
Let us add b24b24 to the expression in the parentheses: 
=(x2bx+b24b24)75 We added b24b24 to the expression 
=(x2bx+b24)+b2475 We put b24 outside the parentheses. 
=(xb2)275+b24 we used the rule a22ab+b2=(ab)2 
The function f's standard form was obtained. The maximum value of 25 is equal to the y-coordinate of the vertex (h,k). We know that k=b2475 
Let us find of b by setting 25 and b2475 equal: 
25=b2475 
100=b24 we put -75 on the other side and added terms. 
400=b2 we multiplied both sides by 4. 
±20=b we found the square root of both sides 
Result: The function has the maximum value equal to 25 for b=±20

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