The Mean Value Theorem states that the function must be continuous and differentiable over the whole x-interval and there must be a point in the derivative where you plug in a number and get 0 out.(f'(c)=0). If a function is constant then the derivative of that function is 0 => any number you put in, you will get 0 out. Thus, using the MVT we deduced that the slope must be zero and since the f(x) is a constant function then the slope IS 0.
The integral of a given function between given integration limits will always be a constant. The integral of a given function between variable limits - for example, from 0 to x - can only be a constant if the function is equal to zero everywhere.
The integral of the density function from the given point upwards.
The function that is given has a constant value and therefore, its slope is 0.
The value that results from the substitution of a given input into an expression or function is the output. The value substituted into an expression or function is an input.
Limits (or limiting values) are values that a function may approach (but not actually reach) as the argument of the function approaches some given value. The function is usually not defined for that particular value of the argument.
The integral of a given function between given integration limits will always be a constant. The integral of a given function between variable limits - for example, from 0 to x - can only be a constant if the function is equal to zero everywhere.
The integral of the density function from the given point upwards.
The function that is given has a constant value and therefore, its slope is 0.
Substitute the given value for the argument of the function.
Basic calculus is about the study of functions. The two main divisions of calculus are differentiation and integration. Differentiation has to do with finding the tangent line to a function at any given point on the function. Integration has to do with finding the area under (or above) a curve. Other topics covered in calculus include: Differential equations Approximations of functions (linear approximation, series, Taylor series) Function analysis (Intermediate Value Theorem, Mean Value Theorem)
The value that results from the substitution of a given input into an expression or function is the output. The value substituted into an expression or function is an input.
"thales" has given this bpt theorem.
Limits (or limiting values) are values that a function may approach (but not actually reach) as the argument of the function approaches some given value. The function is usually not defined for that particular value of the argument.
It does not change its value whatever the value of the variables, under a given set of conditions.
An algebraic letter. e/g 5a 'a' is a non numeric constant. Remember in algebraic , when a letter is given , it means that the value of the letter is a constant, but the value is unknown .
The functions are periodic and so, given any value (within the range) the function can take the value several times, Graphing the function can help you determine secondary points at which the function takes a given value.
The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.