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If x is real, find the maximum value of (-x2 + 3x + 7)
- a)36/5
- b)37/7
- c)37/4
- d)36/7
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If x is real, find the maximum value of (-x2 + 3x + 7)a)36/5b)37/7c)37...
Given Equation:
- x is real, find the maximum value of (-x^2 + 3x + 7)
Step 1: Find the vertex of the parabola
- The given equation is in the form of a quadratic equation, -x^2 + 3x + 7.
- To find the maximum value, we need to find the vertex of the parabola represented by this equation.
- The x-coordinate of the vertex is given by the formula: x = -b/2a, where a=-1 and b=3 in this case.
- Substituting the values of a and b, we get x = -3/(2*(-1)) = 3/2.
- Now, substitute x = 3/2 back into the equation to find the maximum value.
Step 2: Calculate the maximum value
- Substitute x = 3/2 into the equation: (-3/2)^2 + 3*(3/2) + 7
- Simplify the expression to find the maximum value: -9/4 + 9/2 + 7 = 37/4
Therefore, the maximum value of the given equation (-x^2 + 3x + 7) when x is real is 37/4. Hence, the correct answer is option 'C'.
- x is real, find the maximum value of (-x^2 + 3x + 7)
Step 1: Find the vertex of the parabola
- The given equation is in the form of a quadratic equation, -x^2 + 3x + 7.
- To find the maximum value, we need to find the vertex of the parabola represented by this equation.
- The x-coordinate of the vertex is given by the formula: x = -b/2a, where a=-1 and b=3 in this case.
- Substituting the values of a and b, we get x = -3/(2*(-1)) = 3/2.
- Now, substitute x = 3/2 back into the equation to find the maximum value.
Step 2: Calculate the maximum value
- Substitute x = 3/2 into the equation: (-3/2)^2 + 3*(3/2) + 7
- Simplify the expression to find the maximum value: -9/4 + 9/2 + 7 = 37/4
Therefore, the maximum value of the given equation (-x^2 + 3x + 7) when x is real is 37/4. Hence, the correct answer is option 'C'.
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Community Answer
If x is real, find the maximum value of (-x2 + 3x + 7)a)36/5b)37/7c)37...
Given:
(- x2 + 3x + 7)
Concept used:
dy/dx = 0, the value of x gives the minimum value when d2y/dx2 is greater than 0, and gives the maximum value when d2y/dx2 is less than 0
Calculation:
(- x2 + 3x + 7) ----(i)
Differentiating (i),
dy/dx = 0
⇒ - 2x + 3 = 0 ----(ii)
⇒ x = 3/2
By double differentiating equation (ii),
d2y/dx2 = - 2 < 0
That means the maximum value of equation (i) is at x = 3/2
Maximum value of equation (i)
⇒ - 9/4 + 9/2 + 7
⇒ (- 9 + 18 + 28)/4
⇒ 37/4
∴ The maximum value is 37/4.
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If x is real, find the maximum value of (-x2 + 3x + 7)a)36/5b)37/7c)37/4d)36/7Correct answer is option 'C'. Can you explain this answer?
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